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Inferring Boolean functions via higher-order correlations

Author

Listed:
  • Markus Maucher
  • David Kracht
  • Steffen Schober
  • Martin Bossert
  • Hans Kestler

Abstract

Both the Walsh transform and a modified Pearson correlation coefficient can be used to infer the structure of a Boolean network from time series data. Unlike the correlation coefficient, the Walsh transform is also able to represent higher-order correlations. These correlations of several combined input variables with one output variable give additional information about the dependency between variables, but are also more sensitive to noise. Furthermore computational complexity increases exponentially with the order. We first show that the Walsh transform of order 1 and the modified Pearson correlation coefficient are equivalent for the reconstruction of Boolean functions. Secondly, we also investigate under which conditions (noise, number of samples, function classes) higher-order correlations can contribute to an improvement of the reconstruction process. We present the merits, as well as the limitations, of higher-order correlations for the inference of Boolean networks. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Markus Maucher & David Kracht & Steffen Schober & Martin Bossert & Hans Kestler, 2014. "Inferring Boolean functions via higher-order correlations," Computational Statistics, Springer, vol. 29(1), pages 97-115, February.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:1:p:97-115
    DOI: 10.1007/s00180-012-0385-2
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    References listed on IDEAS

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    1. Markus W. Covert & Eric M. Knight & Jennifer L. Reed & Markus J. Herrgard & Bernhard O. Palsson, 2004. "Integrating high-throughput and computational data elucidates bacterial networks," Nature, Nature, vol. 429(6987), pages 92-96, May.
    2. Hans Kestler & Ludwig Lausser & Wolfgang Lindner & Günther Palm, 2011. "On the fusion of threshold classifiers for categorization and dimensionality reduction," Computational Statistics, Springer, vol. 26(2), pages 321-340, June.
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    Cited by:

    1. Harald Binder & Hans Kestler & Matthias Schmid, 2014. "Proceedings of Reisensburg 2011," Computational Statistics, Springer, vol. 29(1), pages 1-2, February.

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